The sampling of the near-field radiated by a planar source observed over a finite planar aperture is addressed. To this end, we employ the warping method that amounts to properly change the observation variables and finding the sampling points as those that allow to approximate the singular values of the radiation operator up to the so-called number of degrees of freedom. In particular, the warping transformations allow to approximate the kernel function of the relevant operator as a band-limited function and hence the sampling theorem is adopted to devise the discretization scheme. Here, we generalize the warping method to the full vector case and introduce a spatially varying oversampling strategy that allows to deal with measurement apertures which are larger than the source. It is shown that the sampling points need to be non-uniformly arranged across the measurement aperture but their number is generally much lower than classical half-wavelength sampling. A numerical analysis is included to support the theoretical arguments. Finally, numerical experiment-based results concerning the radiation pattern estimation of a planar array antenna are presented. To this end, experimental data collected under a uniform half-wavelength sampling scheme are first interpolated over the required non-uniform grid and then processed to obtain the radiation pattern.
